4 JAN FEB 2021 COS4852 Question 3: Neural Networks -[19] Consider the 8 instances below, with positive instances marked as P, and negative instance as N: (-3,-1) B. (-1,2) Ps (1,3) . (3,1) Ni (-2,-3) N2 (0.5, -3.5) NE (4,-2) N4 (2,-1) Figure 1 shows the instances as well as the decision surface/hyperplane for a single neuron Perceptron. a ." - NE Figure 1: 8 instances and the hyperplane of a Perceptron. The cut-off points of the hyperplane on the axes are at (2,0) and (0,-1). (a) Calculate the values of the weights of the Perceptron, using the position of the decision surface/hyperplane. (10) [TURN PAGE ... ] 5 5 JAN FEB 2021 COS4852 T (b) Design a neural network, using one or more Perceptron neurons, for the Boolean function fi, defined as in Table 3. yfir,y) -2 -2 -1 -2 +2 +2 -2 +2 +2 +1 +1 +1 Table 3: Function fi(1,y). Use the threshold activation function (as defined in the Appendix on p. 7) in your calculations. Plot the points of Table 3 in the input space of fi. Show the decision boundary used in your calculations. Calculate the weight values for the connections in your neural network. (9) 4 JAN FEB 2021 COS4852 Question 3: Neural Networks -[19] Consider the 8 instances below, with positive instances marked as P, and negative instance as N: (-3,-1) B. (-1,2) Ps (1,3) . (3,1) Ni (-2,-3) N2 (0.5, -3.5) NE (4,-2) N4 (2,-1) Figure 1 shows the instances as well as the decision surface/hyperplane for a single neuron Perceptron. a ." - NE Figure 1: 8 instances and the hyperplane of a Perceptron. The cut-off points of the hyperplane on the axes are at (2,0) and (0,-1). (a) Calculate the values of the weights of the Perceptron, using the position of the decision surface/hyperplane. (10) [TURN PAGE ... ] 5 5 JAN FEB 2021 COS4852 T (b) Design a neural network, using one or more Perceptron neurons, for the Boolean function fi, defined as in Table 3. yfir,y) -2 -2 -1 -2 +2 +2 -2 +2 +2 +1 +1 +1 Table 3: Function fi(1,y). Use the threshold activation function (as defined in the Appendix on p. 7) in your calculations. Plot the points of Table 3 in the input space of fi. Show the decision boundary used in your calculations. Calculate the weight values for the connections in your neural network. (9)